FOXBOROUGH, Mass. — Tim Tebow hasn’t given up hope of playing in the NFL after being cut by the New England Patriots.

“I will remain in relentless pursuit of continuing my lifelong dream of being an NFL quarterback,” he tweeted Saturday.

He has now been let go by his third team in 18 months. With the regular season just five days away, his chances of immediately catching on with another team seem slim.

Tebow thanked owner Robert Kraft, coach Bill Belichick and offensive coordinator Josh McDaniels after failing to survive New England’s mandatory roster cut to 53 players. He also thanked the “entire Patriots organization for giving me the opportunity to be a part of such a classy organization.”

Tebow’s stay with the Patriots lasted just under 12 weeks and could be the end of his NFL career. The Heisman Trophy winner played in three of New England’s four preseason games and was sacked four times in the finale, a 28-20 win over the New York Giants on Thursday night.

The Patriots have carried just two quarterbacks in three of the past four seasons. And with Ryan Mallett entrenched as the backup to Tom Brady, Tebow’s challenge was a difficult one, even before the preseason started. Then, he went out and posted a quarterback rating of just 47.2 and threw two touchdown passes to go with two interceptions and seven sacks.

When New England signed him June 11, it appeared Belichick might find other positions for him, given his versatility and mobility. But Tebow never worked out with any unit other than the quarterbacks.

After sitting out the third preseason game, a 40-9 loss at Detroit, Tebow completed 6 of 11 passes for 91 yards with two touchdowns and one interception against the Giants. He also ran six times for 30 yards.

“It’s not just one game (that matters),” Belichick said Friday about the player evaluation process, “although every game is important. But the body of work, the camp, the rate of improvement, the ability to do the things that players are going to be asked to do at their respective positions (also matters).”

Tebow previously played for the Denver Broncos and New York Jets. In college, he was a part of two national championship teams at Florida.

Signing Tebow posed little financial risk to the Patriots. Two people with knowledge of the deal told The Associated Press that Tebow signed for two years but with no guaranteed money. One person said he would make the veteran’s minimum salary, $630,000 in 2013, with incentives.

Tebow’s last play with the Patriots, and perhaps in the NFL, was a 9-yard touchdown to rookie free agent Quentin Sims with six seconds left against the Giants.

After the game, Tebow said he wasn’t sure his performance would be enough to keep him on the team.

But he didn’t plan to worry. He would “go to sleep when I get home, wake up, come work out, watch the film,” he said. “See what I did good, see what I did bad, try to learn from it and get better.”

Tebow became the center ring of a media circus last season with the Jets as quarterback Mark Sanchez struggled. But Tebow threw just eight passes that season and was released April 29. He wasn’t picked up until six weeks later, when he took part in the first day of the Patriots’ three-day minicamp.

With Brady at quarterback and Belichick adept at handling distractions, Tebow’s profile was much lower in New England.

“First and foremost, I just want to thank the Patriots for giving me an opportunity,” Tebow said after his first practice. “I’m looking forward to working hard every single day and getting a lot better and learning under some great people. So that’s all I got, but thank you all so much and God bless. I’m sure we’ll be talking more soon.”

The Patriots limited the attention on Tebow that day by allowing him to speak for just 40 seconds and to take no questions.

He was praised this week by Belichick and Kraft, but neither gave an indication of whether he would make the team.

“I learned very early on in my career at Florida to worry about what I can control and the things that I can’t control I’m not going to spend time worrying about,” Tebow said Monday. “But I can control my attitude, my focus every single day and those are the things that I’m going to worry about.”

In three exhibition games, he completed 11 of 30 passes for 145 yards and ran 16 times for 91 yards.

Tebow was drafted by Denver in the first round with the 25th overall pick in 2010. He started the last three of the nine games he played as a rookie then didn’t start again until the sixth game in 2011. He was 7-1 in his first eight starts in the regular season before losing the last three. But in the wild-card playoff game against the Pittsburgh Steelers, he and Demaryius Thomas connected on an 80-yard touchdown pass on the first play of overtime for a 29-23 win.

But six days later, Tebow completed just 9 of 26 passes for 136 yards in a 45-10 loss to the Patriots.